How do I group by min value in one field of table, keeping all the values from that same row?

You'll have to execute this with subqueries.

Select * from  yourtable t  inner join     (   Select field1, min(field2) as minField2         from yourtable         group by field1     ) xx     on t.field1 = xx.field1 and t.field2 = xx.minfield2

Now, if you have multiple rows for a minimal field2 value, then you'll have dupes...If you don't want that (i.e. you want the minimal value of field3 for every minimal value of field2) in that case, you'd need another sub query:

Select outert.field1, outert.field2, outert.field3from yourtable outert inner join (  Select t.field1, xx.minfield2, min(field3) as minfield3 from  yourtable t  inner join     (   Select field1, min(field2) as minField2         from yourtable         group by field1     ) xx     on t.field1 = xx.field1 and t.field2 = xx.minfield2 group by t.field1, xx.minfield2) outerxon outerx.field1 = outert.field1 and outerx.field2 = outert.minfield2and outerx.field3 = outert.minfield3 

As you can see there is a solution that works using only standard SQL, but it's long and complicated.

Note that it's also possible to write a "Hello, world!" program that works correctly in three different programming languages. Doing this doesn't usually add any value to your program though. It's much easier just to write the program three times, tailored to the specific syntax of each language.

I think with SQL it is often better to forget trying to find a solution that works in all RDBMS and use the specific vendor extensions and idioms that make queries like this easier. For example in MS SQL Server, you could do something like this:

SELECT Field1, Field2, Field3FROM (    SELECT *, ROW_NUMBER() OVER (PARTITION BY field1 ORDER BY field2) AS rn    FROM table1) AS T1WHERE rn = 1

Anyway, you already have a general solution, so I just thought I'd offer this alternative viewpoint.